Optimal. Leaf size=66 \[ \frac{2 a^3}{b^4 \sqrt{a+b x}}+\frac{6 a^2 \sqrt{a+b x}}{b^4}-\frac{2 a (a+b x)^{3/2}}{b^4}+\frac{2 (a+b x)^{5/2}}{5 b^4} \]
[Out]
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Rubi [A] time = 0.0495814, antiderivative size = 66, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{2 a^3}{b^4 \sqrt{a+b x}}+\frac{6 a^2 \sqrt{a+b x}}{b^4}-\frac{2 a (a+b x)^{3/2}}{b^4}+\frac{2 (a+b x)^{5/2}}{5 b^4} \]
Antiderivative was successfully verified.
[In] Int[x^3/(a + b*x)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 10.9244, size = 63, normalized size = 0.95 \[ \frac{2 a^{3}}{b^{4} \sqrt{a + b x}} + \frac{6 a^{2} \sqrt{a + b x}}{b^{4}} - \frac{2 a \left (a + b x\right )^{\frac{3}{2}}}{b^{4}} + \frac{2 \left (a + b x\right )^{\frac{5}{2}}}{5 b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(b*x+a)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0239952, size = 45, normalized size = 0.68 \[ \frac{2 \left (16 a^3+8 a^2 b x-2 a b^2 x^2+b^3 x^3\right )}{5 b^4 \sqrt{a+b x}} \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(a + b*x)^(3/2),x]
[Out]
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Maple [A] time = 0.009, size = 42, normalized size = 0.6 \[{\frac{2\,{b}^{3}{x}^{3}-4\,a{b}^{2}{x}^{2}+16\,{a}^{2}bx+32\,{a}^{3}}{5\,{b}^{4}}{\frac{1}{\sqrt{bx+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(b*x+a)^(3/2),x)
[Out]
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Maxima [A] time = 1.34211, size = 76, normalized size = 1.15 \[ \frac{2 \,{\left (b x + a\right )}^{\frac{5}{2}}}{5 \, b^{4}} - \frac{2 \,{\left (b x + a\right )}^{\frac{3}{2}} a}{b^{4}} + \frac{6 \, \sqrt{b x + a} a^{2}}{b^{4}} + \frac{2 \, a^{3}}{\sqrt{b x + a} b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x + a)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.209178, size = 55, normalized size = 0.83 \[ \frac{2 \,{\left (b^{3} x^{3} - 2 \, a b^{2} x^{2} + 8 \, a^{2} b x + 16 \, a^{3}\right )}}{5 \, \sqrt{b x + a} b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x + a)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 8.93163, size = 1538, normalized size = 23.3 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(b*x+a)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.204771, size = 82, normalized size = 1.24 \[ \frac{2 \, a^{3}}{\sqrt{b x + a} b^{4}} + \frac{2 \,{\left ({\left (b x + a\right )}^{\frac{5}{2}} b^{16} - 5 \,{\left (b x + a\right )}^{\frac{3}{2}} a b^{16} + 15 \, \sqrt{b x + a} a^{2} b^{16}\right )}}{5 \, b^{20}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x + a)^(3/2),x, algorithm="giac")
[Out]